Genetic Corn
Chi-square tests let us determine whether two sets of proportions are similar. For
example, in the set of data below, let’s see whether these two forest site are similar in their
proportions of tree species. The chart is set up to do a chi-square operation for you.
Species
Site 1
11.6
14.9
49.3
20.9
3.2
oak
maple
persimmon
elm
hickory
Site 2
10.9
16.1
46.9
21.3
4.7
d (or e-o)
.7
-1.2
2.4
-.4
-1.5
d2
.49
1.44
5.76
.16
2.25
X
d2/e
.042
.097
.117
.007
.703
.966
We find that the X2 value is 0.966. Now we need to determine the degrees of freedom in
this comparison. This is equal to the number of data classes (in this case, species) minus 1
(5-1, or 4). Now determine the amount of certainty you need for the comparison. In most
cases, 0.05 for a p value is acceptable. This means that there is only a 5% chance that the
samples are different by chance alone. (Or a 95% chance that any differences found are
real differences.)
Chi-Square Table
df
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
p = 0.05
3.84
5.99
7.82
9.49
11.07
12.59
14.07
15.51
16.92
18.31
19.68
21.03
22.36
23.69
25.00
Copyright 2003, John McWilliams
p = 0.01
6.64
9.21
11.35
13.28
15.09
16.81
18.48
20.09
21.67
23.21
24.73
26.22
27.69
29.14
30.58
p = 0.001
10.83
13.82
16.27
18.47
20.52
22.46
24.32
26.13
27.88
29.59
31.26
32.91
34.53
36.12
37.70
Note that in order for two sets of
data to be considered significantly
different, (at the p = .05 level and
with 4 degrees of freedom) the X2
value would have to be at least
9.49. Our X2 value was 0.966-much less than that value.
Therefore, we cannot conclude
that the proportions of species in
the two areas are significantly
different.
In genetics, we often use chi-square analyses to tell us whether an observed set of
phenotype proportions is similar to what we would expect, given a particular genetic
cross. For example, if a certain cross between two parents should give us a 3 to 1 ratio of
two traits, we can see how close the actual offspring are to that 3:1 ratio.
The corn you have is the result of a dihybrid cross involving two unrelated traits:
purple color (P, dominant)
yellow color (p, recessive)
starch-containing (S, dominant)
sugar-containing (s, recessive)
The parents of the corn were both
PpSs
Your task…Determine whether the color and texture of the kernels on your corn ear were
produced by genetics or some random environmental factor.
Use this chart to calculate your corn chi-square…
Species
purple/starchy
purple/sugary
yellow/starchy
yellow/sugary
e
o
d (or e-o)
d2
d2/e
chi value =
Turn in one of these data pages for you and your partner. No report, but on
the next exam you’ll be expected to interpret a chi2 test, given similar data
and a chi2 chart.
Copyright 2003, John McWilliams